Coccidia is pretty common. My vet said almost all bunnies from shelters have it, but it’s usually at very low levels. It is very host specific, so you don’t need to worry about your cat getting it. Does she have diarrhea or a very high number of coccidia? Many rabbits are asymptomatic carriers of the parasite, but young rabbits usually need treatment as they can have symptoms.

You can help the treatment by keeping her litter box and area very clean and disinfected, as it is spread through feces. Vinegar probably won’t be strong enough….This info is from medirabbit (http://www.medirabbit.com/EN/GI_diseases/Protozoal_diseases/Cocc_en.htm):
“Treatment of the environment is important (e.g. 10% ammonia). Water crocks and feed hoppers should be disinfected and remain free of rabbit feces. When treating a carpet, vacuum first in order to further penetration of the anticoccidial product. During treatment of the environment, rabbits should be kept in another part of the home to avoid the danger of contact with the products and possible intoxication.”

As for the medicine, I will usually put the bunny on my lap on a towel, with their head facing away from me. Use your non-dominant hand to hold their head (thumb behind the ears, fingers under the jaw). With your dominant hand, stick the syringe under their upper lip, right behind the incisors. There is a pocket behind the incisors but before the molars. Aim for that pocket. Dispense the medicine slowly so she has time to swallow.

This video gives good tips https://www.youtube.com/watch?v=xaHtUy4EX5s
They use a different option for holding the bunny, but it’s basically the same.

That’s good that she isn’t showing symptoms. Your vet is likely treating it as a precaution because she is so young.